Magnetic field measurement method and magnetic field measurement apparatus

ABSTRACT

In a magnetic field measurement apparatus, a light source irradiates a gas cell with linearly polarized light serving as pump light and probe light in a Z axis direction, and a magnetic field generator applies alternating magnetic fields which have the same cycle and different phases to the gas cell in each of X axis and Y axis directions. A calculation controller calculates a magnetic field C (C x , C y , C z ) of a measurement region using X axis and Y axis components A x  and A y  of the alternating magnetic fields, and a spin polarization degree M x  corresponding to a measurement value W −  from a magnetic sensor.

BACKGROUND

1. Technical Field

The present invention relates to a magnetic field measurement method using light and a magnetic field measurement apparatus.

2. Related Art

A magnetic field measurement apparatus using light can measure one component of a weak magnetic field generated from a living body, such as a magnetic field (heart magnetic field) from the heart or a magnetic field (brain magnetic field) from the brain, and is expected to be applied to a medical image diagnostic apparatus or the like. In such a magnetic field measurement apparatus, pump light and probe light are applied to a gas cell in which gaseous alkali metals or the like are sealed. Atoms enclosed in the gas cell are excited by the pump light so as to be spin-polarized, and a polarization plane of the probe light which is transmitted through the gas cell is rotated according to a magnetic field due to the magneto-optical effect. One component of a magnetic field is measured by measuring rotation angles of the polarization plane of the probe light before and after being transmitted through the gas cell (for example, JP-A-2013-108833).

In a general magnetic field measurement apparatus using an optical pumping method of the related art, a detection axis of a magnetic field is located in the same direction, and if directions of the detection axis and the magnetic field are different from each other, a projection component of the magnetic field onto the detection axis is measured. However, a magnetic field which is actually distributed in a space is expressed as three-dimensional vectors, and if a magnetic field is to be measured more accurately, magnetic fields in three-axis directions such as three orthogonal XYZ axes are preferably measured. Since a detection axis is located in a direction corresponding to an irradiation direction of probe light, it is necessary to cause the respective irradiation directions to be accurately perpendicular to each other in a case where the detection axes are increased by simply increasing the irradiation direction of the probe light. If an irradiation direction is tilted with respect to an expected direction, a detection axis is thus also tilted, and, as a result, errors occur in a measured value of a magnetic field which is expressed as three-dimensional vectors. In a case where the probe light is incident to the gas cell from three-axis directions, a configuration of the apparatus is complicated and is thus unlikely to be implemented.

SUMMARY

An advantage of some aspects of the invention is that magnetic fields in a plurality of directions can be measured while applying probe light in one direction, or a magnetic field can be measured with high accuracy in magnetic field measurement using an optical pumping method.

Application Example 1

Application Example 1 is directed to a magnetic field measurement method of measuring a magnetic field of a measurement region in a magnetic field measurement apparatus in which a first direction, a second direction, and a third direction are perpendicular to each other and which includes a light source that emits light, a medium through which the light passes in the third direction and that changes optical characteristics depending on a magnetic field of the measurement region, a photodetector that detects the optical characteristics, a first magnetic field generator that applies a magnetic field in the first direction to the medium, and a second magnetic field generator that applies a magnetic field in the second direction to the medium. The method includes causing the first magnetic field generator to generate a first alternating magnetic field; causing the second magnetic field generator to generate a second alternating magnetic field which has the same cycle as a cycle of the first alternating magnetic field and has δ as a phase difference with the first alternating magnetic field; and calculating the magnetic field of the measurement region using a detection result from the photodetector, the first alternating magnetic field, and the second alternating magnetic field.

In the magnetic field measurement method of this application example, it is possible to calculate a magnetic field of the measurement region through irradiation with light in only one direction such as the third direction (Z direction). Specifically, the first alternating magnetic field which is a magnetic field in the first direction (X direction) perpendicular to the third direction (Z direction) which is an irradiation direction of light, and the second alternating magnetic field which is a magnetic field in the second direction (Y direction) perpendicular to the third direction (Z direction) and the first direction (X direction) and has the same cycle as that of the first alternating magnetic field and has δ as a phase difference with the first alternating magnetic field, are applied to the medium which changes optical characteristics of the light according to a magnetic field of the measurement region. The magnetic field of the measurement region is calculated using a detection result of the optical characteristics of the light, and the first alternating magnetic field, and the second alternating magnetic field.

Application Example 2

As Application Example 2, the magnetic field measurement method according to Application Example 1 may be configured such that the calculating of the magnetic field of the measurement region includes calculating a magnetization value indicating a component in the first direction of a magnetization vector of the medium when the first alternating magnetic field and the second alternating magnetic field are generated, or a value corresponding to the magnetization value, on the basis of the detection result from the photodetector.

In the magnetic field measurement method of this application example, the magnetization value indicating the component in the first direction (X direction) of the magnetization vector of the medium is calculated on the basis of the detection result of the optical characteristics of the light, and the magnetic field of the measurement region is calculated using the magnetization value, the first alternating magnetic field, and the second alternating magnetic field.

Application Example 3

As Application Example 3, the magnetic field measurement method according to Application Example 2 may be configured such that the calculating of the magnetic field of the measurement region is performed using three or more different combinations of the first alternating magnetic field and the second alternating magnetic field.

In the magnetic field measurement method of this application example, it is possible to calculate the magnetic field of the measurement region using the combinations of the magnetization values, values of the first alternating magnetic field, and values of the second alternating magnetic field, and having the different magnetization values at three or more timings.

Application Example 4

As Application Example 4, the magnetic field measurement method according to Application Example 3 may be configured such that the calculating of the magnetic field of the measurement region is performed by applying the following Equation 1 to each of the combinations.

$\begin{matrix} {\; {M_{x} = {\frac{c}{a} \cdot \frac{\begin{matrix} {{C_{x}C_{y}} + {C_{x}A_{20}{f\left( {{\omega \; t} + \delta} \right)}} + {C_{y}A_{10}f\left( {\omega \; t} \right)} +} \\ {{A_{10}{f\left( {\omega \; t} \right)}A_{20}{f\left( {{\omega \; t} + \delta} \right)}} + {aC}_{z}} \end{matrix}}{\begin{matrix} {a^{2} + C_{x}^{2} + C_{y}^{2} + C_{z}^{2} + {2\; C_{x}A_{10}f\left( {\omega \; t} \right)} +} \\ {{2\; C_{y}A_{20}{f\left( {{\omega \; t} + \delta} \right)}} + {A_{10}^{2}{f\left( {\omega \; t} \right)}^{2}} + {A_{20}^{2}{f\left( {{\omega \; t} + \delta} \right)}^{2}}} \end{matrix}}}}} & (1) \end{matrix}$

In the equation, the magnetic field of the measurement region is expressed by C=(C_(x), C_(y), C_(z)); x, y, and z respectively indicate spatial coordinates in the first direction, the second direction, and the third direction; M_(x) indicates the magnetization value; a and c are constants; A₁₀f (ωt) indicates the first alternating magnetic field; and A₂₀f (ωt+δ) indicates the second alternating magnetic field, in which δ is the phase difference, ω is an angular frequency of the first alternating magnetic field and the second alternating magnetic field, and t is time.

In the magnetic field measurement method of this application example, the magnetic field (C_(x), C_(y), C_(z)) of the measurement region of the medium, which is a three-dimensional vector, can be calculated by solving simultaneous equations, the simultaneous equations being defined by three or more equations obtained by assigning respective values of combinations of the magnetization values, the values of the first alternating magnetic field, and the values of the second alternating magnetic field, to Equation 1.

Application Example 5

An alternating magnetic field in the second direction and an alternating magnetic field in the first direction may be defined specifically as follows. For example, as Application Example 5, the magnetic field measurement method may be configured such that the phase difference is π/2.

Application Example 6

As Application Example 6, the magnetic field measurement method may be configured such that the first alternating magnetic field and the second alternating magnetic field have trigonometric function waves.

Application Example 7

As Application Example 7, the magnetic field measurement method may be configured such that the first alternating magnetic field and the second alternating magnetic field have triangular waves.

Application Example 8

As Application Example 8, the magnetic field measurement method may be configured such that the first alternating magnetic field and the second alternating magnetic field have rectangular waves.

Application Example 9

Application Example 9 is directed to a magnetic field measurement method of measuring a magnetic field of a measurement region in a magnetic field measurement apparatus in which a first direction, a second direction, and a third direction are perpendicular to each other and which includes a light source that emits light, a medium through which the light passes in the third direction and that changes optical characteristics depending on a magnetic field of the measurement region, a photodetector that detects the optical characteristics, a first magnetic field generator that applies a magnetic field in the first direction to the medium, a second magnetic field generator that applies a magnetic field in the second direction to the medium, and a third magnetic field generator that applies a magnetic field in the third direction to the medium. The method includes causing the first magnetic field generator to generate a first alternating magnetic field; causing the second magnetic field generator to generate a second alternating magnetic field which has the same cycle as a cycle of the first alternating magnetic field and has δ as a phase difference with the first alternating magnetic field; a first procedure of calculating the magnetic field of the measurement region as an original magnetic field using a detection result from the photodetector, the first alternating magnetic field, and the second alternating magnetic field; a second procedure of disposing a measurement target object in the measurement region; a third procedure of causing the first magnetic field generator, the second magnetic field generator, and the third magnetic field generator to generate a magnetic field corresponding to a difference between a target magnetic field which is desired to be formed in the measurement region and the original magnetic field; and a fourth procedure of measuring a magnetic field generated by the measurement target object using the detection result from the photodetector in a period in which the third procedure is being performed and the second procedure is completed.

In the magnetic field measurement method of this application example, a magnetic field generated by the measurement target object can be measured in a state in which a predetermined target magnetic field is formed in the measurement region. For example, if the target magnetic field is set to a zero magnetic field in order to cancel out the original magnetic field which enters the measurement region from the outside, it is possible to accurately measure the magnetic field generated by the measurement target object.

Application Example 10

Application Example 10 is directed to a magnetic field measurement method of measuring a magnetic field of a measurement region in a magnetic field measurement apparatus in which a first direction, a second direction, and a third direction are perpendicular to each other and which includes a light source that emits light, a medium through which the light passes in the third direction and that changes optical characteristics depending on a magnetic field of the measurement region, a photodetector that detects the optical characteristics, a first magnetic field generator that applies a magnetic field in the first direction to the medium, a second magnetic field generator that applies a magnetic field in the second direction to the medium, and a third magnetic field generator that applies a magnetic field in the third direction to the medium. The method includes causing the first magnetic field generator to generate a first alternating magnetic field; causing the second magnetic field generator to generate a second alternating magnetic field which has the same cycle as a cycle of the first alternating magnetic field and has δ as a phase difference with the first alternating magnetic field; a first procedure of calculating the magnetic field of the measurement region as the original magnetic field using a detection result from the photodetector, the first alternating magnetic field, and the second alternating magnetic field; a second procedure of disposing a measurement target object in the measurement region; a third procedure of causing the first magnetic field generator to generate a third alternating magnetic field in which a first direction component of a magnetic field corresponding to a difference between a target magnetic field which is desired to be formed in the measurement region and the original magnetic field is added to the first alternating magnetic field, causing the second magnetic field generator to generate a fourth alternating magnetic field in which a second direction component of the magnetic field corresponding to the difference is added to the second alternating magnetic field, and causing the third magnetic field generator to generate a magnetic field having a third direction component of the magnetic field corresponding to the difference; and a fourth procedure of measuring a magnetic field generated by the measurement target object using the detection result from the photodetector, the third alternating magnetic field, and the fourth alternating magnetic field in a period in which the third procedure is being performed and the second procedure is completed.

In the magnetic field measurement method of this application example, a magnetic field generated by the measurement target object can be measured in a state in which a predetermined target magnetic field is formed in the measurement region. For example, if the target magnetic field is set to a zero magnetic field in order to cancel out the original magnetic field which enters the measurement region from the outside, it is possible to accurately measure the magnetic field generated by the measurement target object as a vector quantity.

Application Example 11

Application Example 11 is directed to a magnetic field measurement apparatus in which a first direction, a second direction, and a third direction are perpendicular to each other. The apparatus includes a light source that emits light; a medium through which the light passes in the third direction and that changes optical characteristics depending on a magnetic field of the measurement region; a photodetector that detects the optical characteristics; a first magnetic field generator that applies a magnetic field in the first direction to the medium; a second magnetic field generator that applies a magnetic field in the second direction to the medium; and a calculation controller that causes the first magnetic field generator to generate a first alternating magnetic field, causes the second magnetic field generator to generate a second alternating magnetic field which has the same cycle as a cycle of the first alternating magnetic field and has δ as a phase difference with the first alternating magnetic field, and calculates the magnetic field of the measurement region using a detection result from the photodetector, the first alternating magnetic field, and the second alternating magnetic field.

In the magnetic field measurement apparatus of this application example, it is possible to calculate a magnetic field of the measurement region through irradiation with light in only one direction such as the third direction (Z direction). Specifically, the first alternating magnetic field which is a magnetic field in the first direction (X direction) perpendicular to the third direction (Z direction) which is an irradiation direction of light, and the second alternating magnetic field which is a magnetic field in the second direction (Y direction) perpendicular to the third direction (Z direction) and the first direction (X direction) and has the same cycle as that of the first alternating magnetic field and has δ as a phase difference with the first alternating magnetic field, are applied to the medium which changes optical characteristics of the light according to a magnetic field of the measurement region. The magnetic field of the measurement region is calculated using a detection result of the optical characteristics of the light, and the first alternating magnetic field, and the second alternating magnetic field.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be described with reference to the accompanying drawings, wherein like numbers reference like elements.

FIG. 1 is a schematic side view illustrating an example of a configuration of a magnetic field measurement apparatus according to the present embodiment.

FIG. 2 is a schematic diagram illustrating a configuration of a magnetic field generator according to the present embodiment, and, specifically, is a diagram viewed from a Y direction.

FIG. 3 is a schematic diagram illustrating the configuration of the magnetic field generator according to the present embodiment, and, specifically, is a diagram viewed from an X direction.

FIG. 4 is a schematic diagram illustrating the configuration of the magnetic field generator according to the present embodiment, and, specifically, is a diagram viewed from a Z direction.

FIG. 5 is a schematic diagram illustrating a configuration of a magnetic sensor according to the present embodiment, and, specifically, is a plan view viewed from the Z direction.

FIG. 6 is a schematic diagram illustrating the configuration of the magnetic sensor according to the present embodiment, and, specifically, is a side view viewed from the Y direction.

FIG. 7 is a functional configuration diagram illustrating a calculation controller according to the present embodiment.

FIG. 8 is a diagram for explaining an alignment in a case where there is no magnetic field.

FIG. 9 is a diagram for explaining a change in the alignment due to a magnetic field.

FIG. 10 is a diagram for explaining a change in a polarization plane of linearly polarized light due to transmission into a gas cell.

FIG. 11 is a diagram for explaining a change in a polarization plane of linearly polarized light due to transmission into a gas cell.

FIG. 12 is a diagram illustrating a relationship between an alignment azimuth angle θ and a detection result of probe light.

FIG. 13 is a flowchart illustrating a flow of a magnetic field measurement process according to the present embodiment.

FIG. 14 is a graph illustrating an example of a spin polarization degree in a case where an artificial magnetic field in Example 1 has a trigonometric function wave.

FIG. 15 is a graph illustrating an example of a spin polarization degree in a case where an artificial magnetic field in Example 2 has a triangular wave.

FIG. 16 is a graph illustrating an example of a spin polarization degree in a case where an artificial magnetic field in Example 3 has a sawtooth wave.

FIG. 17 is a graph illustrating an example of a spin polarization degree in a case where an artificial magnetic field in Example 4 has a rectangular wave.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

Hereinafter, an embodiment will be described with reference to the drawings.

In addition, respective members in the drawings are illustrated in different scales in order to be recognizable in the drawings.

Configuration of Magnetic Field Measurement Apparatus

First, a configuration example of a magnetic field measurement apparatus according to the present embodiment will be described. FIG. 1 is a schematic side view illustrating an example of a configuration of a magnetic field measurement apparatus according to the present embodiment. FIG. 2 is a schematic diagram illustrating a configuration of a magnetic field generator according to the present embodiment, and, specifically, is a diagram viewed from a Y direction. FIG. 3 is a schematic diagram illustrating the configuration of the magnetic field generator according to the present embodiment, and, specifically, is a diagram viewed from an X direction. FIG. 4 is a schematic diagram illustrating the configuration of the magnetic field generator according to the present embodiment, and, specifically, is a diagram viewed from a Z direction. FIG. 5 is a schematic diagram illustrating a configuration of a magnetic field sensor according to the present embodiment, and, specifically, is a plan view viewed from the Z direction. FIG. 6 is a schematic diagram illustrating the configuration of the magnetic field sensor according to the present embodiment, and, specifically, is a side view viewed from the Y direction. FIG. 7 is a functional configuration diagram illustrating a calculation controller according to the present embodiment.

A magnetic field measurement apparatus 1 illustrated in FIG. 1 is a measurement apparatus which measures a magnetic field generated by a measurement target object as a vector quantity. An apparatus which measures some information (for example, one component, magnitude, presence or absence, or the like) of the magnetic field generated by the measurement target object is referred to as a magnetism measurement apparatus. In the present embodiment, it is assumed that a measurement target object is the human body (subject), and a magnetic field generated by the measurement target object is a heart magnetic field (a magnetic field generated due to electrophysiological activity of the heart) or a brain magnetic field. Herein, as an example, a description will be made of a case where the magnetic field measurement apparatus 1 is a measurement apparatus which measures the heart magnetic field as a vector quantity.

The magnetic field measurement apparatus 1 is an apparatus which measures a magnetic field using an optical pumping method, and is a so-called one-beam type using pump light and probe light together. The magnetic field measurement apparatus 1 is not limited to the one-beam type, and may have a so-called two-beam type configuration in which a light source for applying pump light and a light source for applying probe light are separately provided. As illustrated in FIG. 1, the magnetic field measurement apparatus 1 includes a foundation 3, a table 4, a magnetic shield device 6, a magnetic field generator 8, a magnetic sensor 10, and a calculation controller 30 (refer to FIG. 7).

In the magnetic sensor 10 illustrated in FIG. 6, a direction (irradiation direction) of laser light (also referred to as irradiation light) 18 a emitted from a light source 18 that passes through a gas cell 12 is assumed to be a third direction (the Z direction in the present embodiment). An oscillation direction of a linearly polarized light component of the irradiation light is assumed to be a second direction (the Y direction in the present embodiment). A direction perpendicular to the second direction (Y direction) and the third direction (Z direction) is assumed to be a first direction (the X direction in the present embodiment). The first direction (X direction), the second direction (Y direction), and the third direction (Z direction) are used as axial directions of an orthogonal coordinate system, and are hereinafter respectively referred to as an X axis direction, a Y axis direction, and a Z axis direction.

In FIG. 1, the Z axis direction is a vertical direction, and is a height direction (upward and downward directions in FIG. 1) of the magnetic field measurement apparatus 1. The X axis direction and the Y axis direction are horizontal directions, and are directions in which upper surfaces of the foundation 3 and the table 4 extend. It is assumed that a height direction (left and right directions in FIG. 1) of a subject 9 which horizontally lies is along the X axis direction. Therefore, a direction intersecting the height direction of the subject 9 (a direction which is directed out of the plane of FIG. 1) is the Y axis direction.

The foundation 3 is disposed on a bottom surface inside the magnetic shield device 6 (main body portion 6 a) and extends to the outside of the main body portion 6 a in the X axis direction which is a direction in which the subject 9 can be moved. The table 4 includes a first table 4 a, a second table 4 b, and a third table 4 c. The first table 4 a which is moved in the X axis direction by a linear motion mechanism 3 a is provided on the foundation 3. The second table 4 b which is lifted in the Z axis direction by a lifting device (not illustrated) is provided on the first table 4 a. The third table 4 c which is moved on a rail in the Y axis direction by a linear motion mechanism (not illustrated) is provided on the second table 4 b.

The magnetic shield device 6 includes the square tubular main body portion 6 a having an opening 6 b. The inside of the main body portion 6 a is hollow, and a sectional shape of a plane (a plane of a Y-Z section perpendicular to the X axis direction) formed by the Y axis direction and the Z axis direction is a substantially square shape. When a heart magnetic field is measured, the subject 9 is accommodated inside the main body portion 6 a in a lying on the table 4. The main body portion 6 a extends in the X axis direction and thus functions as a passive magnetic shield.

The foundation 3 protrudes out of the opening 6 b of the main body portion 6 a in the +X direction. As a size of the magnetic shield device 6, a length thereof in the X axis direction is about 200 cm, for example, and one side of the opening 6 b is about 90 cm. The subject 9 laid down on the table 4 can be moved so as to come in and out of the magnetic shield device 6 from the opening 6 b along with the table 4 in the X axis direction on the foundation 3.

The main body portion 6 a of the magnetic shield device 6 is made of a ferromagnetic material having a relative permeability of, for example, several thousands or more, or a conductor having high conductivity. As the ferromagnetic material, permalloy, ferrite, iron, chromium, cobalt-based amorphous metal, or the like may be used. As the conductor having high conductivity, for example, aluminum which has a magnetic field reduction effect due to an eddy current effect may be used. The main body portion 6 a may be formed by alternately stacking a ferromagnetic material and a conductor having high conductivity.

The magnetic field generator 8 is provided inside the main body portion 6 a. The magnetic field generator 8 is constituted of three-axis Helmholtz coils, and can generate predetermined magnetic fields in each of the X axis direction, the Y axis direction, and the Z axis direction in a measurement region 5. In other words, the magnetic field generator 8 includes at least first magnetic field generators 8X which generate a magnetic field in the X axis direction, second magnetic field generators 8Y which generate a magnetic field in the Y axis direction, and preferably further includes third magnetic field generators 8Z which generate a magnetic field in the Z axis direction.

In the present embodiment, the magnetic field generator 8 includes the first magnetic field generators (a pair of Helmholtz coils which oppose each other in the X axis direction) 8X, the second magnetic field generators (a pair of Helmholtz coils which oppose each other in the Y axis direction) 8Y, and the third magnetic field generators (a pair of Helmholtz coils which oppose each other in the Z axis direction) 8Z. A measurement target region of a heart magnetic field in the magnetic field measurement apparatus 1 inside the main body portion 6 a of the magnetic shield device 6 is the measurement region 5. The chest 9 a of the subject 9 as a measurement position and the magnetic sensor 10 are disposed inside the measurement region 5.

As illustrated in FIGS. 2 to 4, each of diameters of the Helmholtz coils 8X, the Helmholtz coils 8Y, and the Helmholtz coils 8Z included in the magnetic field generator 8 is larger than a diameter of the measurement region 5. In other words, the measurement region 5 is included in a region surrounded by the first magnetic field generators 8X, the second magnetic field generators 8Y, and the third magnetic field generators 8Z. The centers of the Helmholtz coils 8X, 8Y and 8Z, the center of the measurement region 5, and the center of the magnetic sensor 10 preferably substantially match each other. In the above-described way, a magnetic field expressed as three-dimensional vectors can be measured with high accuracy in the measurement region 5.

A distance between the pair of opposing Helmholtz coils is preferably more than a diameter of each of the other Helmholtz coils. For example, as illustrated in FIG. 2, a distance between the pair of opposing Helmholtz coils 8X is preferably more than a diameter of each of the Helmholtz coils 8Y and the Helmholtz coils 8Z. In the above-described way, it is possible to generate uniform magnetic fields parallel to the Y axis (or the Z axis) with the pair of Helmholtz coils 8Y (or 8Z). Similarly, a distance between the pair of opposing Helmholtz coils 8Y (or 8Z) is preferably more than a diameter of each of the other Helmholtz coils.

For example, in FIG. 2, in a case where the distance between the pair of opposing Helmholtz coils 8X is less than the diameter of each of the Helmholtz coils 8Y and the Helmholtz coils 8Z, the Helmholtz coils 8X enter a columnar-shape region which has the pair of Helmholtz coils 8Y (or 8Z) as bottoms. Then, magnetic fields formed by the pair of Helmholtz coils 8Y (or 8Z) are distorted, and thus it is unlikely to generate uniform magnetic fields which are parallel to the Y axis (or the Z axis) in the vicinity of the measurement region 5.

The magnetic sensor 10 is fixed to a ceiling of the main body portion 6 a via a supporting member 7. The magnetic sensor 10 measures an intensity component of a magnetic field in the Z axis direction of the measurement region 5. The magnetic sensor 10 measures a magnetic field using an optical pumping method. When a heart magnetic field of the subject 9 is measured, the first table 4 a and the third table 4 c are moved so that the chest 9 a of the subject 9 which is a measurement position is located so as to face the magnetic sensor 10, and the second table 4 b is lifted so that the chest 9 a becomes close to the magnetic sensor 10.

In measurement of a weak magnetic field using the optical pumping type magnetic sensor 10, it is preferable to cancel out a magnetic field (original magnetic field) which comes from the outside due to environments such as the Earth's magnetic field or urban noise which is present in the measurement region 5 in which the gas cell 12 is disposed. This is because, if the original magnetic fields are present, sensitivity for a magnetic field generated by a measurement target object (subject 9) is reduced, or measurement accuracy is reduced, due to an influence thereof. In the present embodiment, the magnetic shield device 6 prevents a magnetic field from entering the measurement region 5 from the outside. The magnetic field generator 8 disposed inside the main body portion 6 a can maintain the vicinity of the measurement region 5 in a low magnetic field state close to zero.

As illustrated in FIG. 5, the magnetic sensor 10 includes the light source 18, the gas cell 12, and photodetectors 14 and 15. The light source 18 outputs the laser light 18 a with a wavelength corresponding to an absorption line of cesium. A wavelength of the laser light 18 a is not particularly limited, but is set to a wavelength of 894 nm corresponding to the D1-line, in the present embodiment. The light source 18 is a tunable laser device, and the laser light 18 a output from the light source 18 is continuous light with a predetermined light amount.

In the present embodiment, the light source 18 is provided in the calculation controller 30. The laser light 18 a emitted from the light source 18 is supplied to a main body of the magnetic sensor 10 via an optical fiber 19. The main body of the magnetic sensor 10 and the optical fiber 19 are connected to each other via an optical connector 20. The laser light 18 a supplied via the optical connector 20 travels in the −Y direction and is incident to a polarization plate 21. The laser light 18 a having passed through the polarization plate 21 is linearly polarized. The laser light 18 a is sequentially incident to a first half mirror 22, a second half mirror 23, a third half mirror 24, and a first reflection mirror 25.

Some of the laser light 18 a is reflected by the first half mirror 22, the second half mirror 23, and the third half mirror 24 so as to travel in the +X direction, and the other light 18 a is transmitted therethrough so as to travel in the −Y direction. The first reflection mirror 25 reflects the entire incident laser light 18 a in the +X direction. An optical path of the laser light 18 a is divided into four optical paths by the first half mirror 22, the second half mirror 23, the third half mirror 24, and the first reflection mirror 25. Reflectance of each mirror is set so that light intensities of the laser light 18 a on the respective optical paths are the same as each other.

Next, as illustrated in FIG. 6, the laser light 18 a is sequentially applied and incident to a fourth half mirror 26, a fifth half mirror 27, a sixth half mirror 28, and a second reflection mirror 29. Some of the laser light 18 a is reflected by the fourth half mirror 26, the fifth half mirror 27, and the sixth half mirror 28 so as to travel in the +Z direction, and the other laser light 18 a is transmitted therethrough so as to travel in the +X direction. The second reflection mirror 29 reflects the entire incident laser light 18 a in the +Z direction.

A single optical path of the laser light 18 a is divided into four optical paths by the fourth half mirror 26, the fifth half mirror 27, the sixth half mirror 28, and the second reflection mirror 29. Reflectance of each mirror is set so that light intensities of the laser light 18 a on the respective optical paths are the same as each other. Therefore, the optical path of the laser light 18 a is divided into the sixteen optical paths. In addition, reflectance of each mirror is set so that light intensities of the laser light 18 a on the respective optical paths are the same as each other.

The sixteen gas cells 12 of four rows and four columns are provided on the respective optical paths of the laser light 18 a on the +Z direction side of the fourth half mirror 26, the fifth half mirror 27, the sixth half mirror 28, and the second reflection mirror 29. The laser light 18 a reflected by the fourth half mirror 26, the fifth half mirror 27, the sixth half mirror 28, and the second reflection mirror 29 pass through the gas cells 12.

The gas cell 12 is a box having a cavity therein, and an alkali metal gas is enclosed in the cavity as a medium for changing optical characteristics of light according to a magnetic field in the measurement region 5 (refer to FIG. 1). The alkali metal is not particularly limited, and potassium, rubidium, or cesium may be used. In the present embodiment, for example, cesium is used as the alkali metal.

A polarization separator 13 is provided on the +Z direction side of each gas cell 12. The polarization separator 13 is an element which separates the incident laser light 18 a into two polarization components of the laser light 18 a, which are perpendicular to each other. As the polarization separator 13, for example, a Wollaston prism or a polarized beam splitter may be used.

The photodetector 14 is provided on the +Z direction side of the polarization separator 13, and the photodetector 15 is provided on the +X direction side of the polarization separator 13. The laser light 18 a having passed through the polarization separator 13 is incident to the photodetector 14, and the laser light 18 a reflected by the polarization separator 13 is incident to the photodetector 15. The photodetector 14 and the photodetector 15 output signals corresponding to an amount of incident laser light 18 a which is received, to the calculation controller 30.

If the photodetectors 14 and 15 generate magnetic fields, this may influence measurement, and thus the photodetectors 14 and 15 may be made of a non-magnetic material. The magnetic sensor 10 includes heaters 16 which are provided on both sides in the X axis direction and both sides in the Y axis direction. Each of the heaters 16 preferably has a structure in which a magnetic field is not generated, and may employ, for example, a heater of a type of performing heating by causing steam or hot air to pass through a flow passage. Instead of using a heater, the gas cell 12 may be inductively heated using a high frequency voltage.

The magnetic sensor 10 is disposed on the +Z direction side of the subject 9 (refer to FIG. 1). A magnetic field vector B (including a target magnetic field vector generated by a measurement target object) which is detected in the measurement region 5 by the magnetic sensor 10 enters the magnetic sensor 10 from the −Z direction side. The magnetic field vector B passes through the fourth half mirror 26 to the second reflection mirror 29, passes through the gas cell 12, then passes through the polarization separator 13, and comes out of the magnetic sensor 10.

The magnetic sensor 10 is a sensor which is called an optical pumping type magnetic sensor or an optical pumping atom magnetic sensor. Cesium in the gas cell 12 is heated and is brought into a gaseous state. The cesium gas is irradiated with the linearly polarized laser light 18 a, and thus cesium atoms are excited, and thus orientations of magnetic moments can be aligned. When the magnetic field vector B passes through the gas cell 12 in this state, the magnetic moments of the cesium atoms precess due to a magnetic field of the magnetic field vector B. This precession is referred to as Larmore precession.

The magnitude of the Larmore precession has a positive correlation with the strength of the magnetic field vector B. In the Larmore precession, a polarization plane of the laser light 18 a is rotated. The magnitude of the Larmore precession has a positive correlation with a change amount of a rotation angle of the polarization plane of the laser light 18 a. Therefore, the strength of the magnetic field vector B has a positive correlation with the change amount of a rotation angle of the polarization plane of the laser light 18 a. The sensitivity of the magnetic sensor 10 is high in the Z axis direction in the magnetic field vector B, and is low in the direction perpendicular to the Z axis direction.

The polarization separator 13 separates the laser light 18 a having passed through the gas cell 12 into two components of linearly polarized light in axial directions (an α axis and a β axis illustrated in FIG. 11) which are perpendicular to each other. One separated linearly polarized light is guided to the photodetector 14, and the other linearly polarized light is guided to the photodetector 15. The photodetector 14 and the photodetector 15 respectively receive the two components of linearly polarized light perpendicular to each other, generate signals corresponding to amounts of the received light, and output the signals to the calculation controller 30. The strength of each of the linearly polarized light is detected, and thus a rotation angle of a polarization plane of the laser light 18 a can be detected. The strength of the magnetic field vector B can be detected on the basis of a change of the rotation angle of the polarization plane of the laser light 18 a.

An electrode constituted of the gas cell 12, the polarization separator 13, the photodetector 14, and the photodetector 15 is referred to as a sensor element 11. In the present embodiment, sixteen sensor elements 11 of four rows and four columns are disposed in the magnetic sensor 10. The number and arrangement of the sensor elements 11 in the magnetic sensor 10 are not particularly limited. The sensor elements 11 may be disposed in three or less rows or five or more rows. Similarly, the sensor elements 11 may be disposed in three or less columns or five or more columns. The larger the number of sensor elements 11, the higher the spatial resolution.

As illustrated in FIG. 7, the calculation controller includes an operation unit 31, a display unit 32, a communication unit 33, a processing unit 40, and a storage unit 50. The operation unit 31 is an input device such as a button switch, a touch panel, a keyboard, or various sensors, and outputs an operation signal corresponding to a performed operation to the processing unit 40. Various input instructions such as an instruction for starting magnetic field measurement are performed using the operation unit 31.

The display unit 32 is a display device such as a liquid crystal display (LCD), and performs various display based on a display signal from the processing unit 40. A measurement result or the like is displayed on the display unit 32. The communication unit 33 is a communication device such as a wireless communication device, a modem, a wired communication cable jack, or a control circuit, and is connected to a predetermined communication line so as to perform communication with external devices.

The processing unit 40 is constituted of a microprocessor such as a central processing unit (CPU) or a graphics processing unit (GPU), or an electronic component such as an application specific integrated circuit (ASIC) or an integrated circuit (IC) memory. The processing unit 40 performs various calculation processes on the basis of a predetermined program or data, an operation signal from the operation unit 31, a measurement signal from the magnetic sensor 10, and the like, so as to control an operation of the calculation controller 30.

The processing unit 40 includes an irradiation control portion 41, a magnetic field generation control portion 42, an original magnetic field calculation portion 43, a bias magnetic field determination portion 44, and a target magnetic field calculation portion 45. The processing unit 40 performs a magnetism measurement process (refer to a flowchart shown in FIG. 13) according to a magnetic field measurement program 51 stored in the storage unit 50.

In the magnetism measurement process according to the present embodiment, prior to measurement of a magnetic field generated by a measurement target object such as the heart or the brain of the human body, an original magnetic field C_(x) of the measurement region 5 is calculated as an initial setting in a state in which the measurement target object is not placed. A magnetic field generated by the measurement target object is measured in a state in which a bias magnetic field which cancels out the original magnetic field C_(x) is generated by the magnetic field generator 8. In other words, measurement of the magnetic field generated by the measurement target object (subject 9) is performed in a state in which an external magnetic field (original magnetic field) coming into the measurement region 5 is reduced.

The irradiation control portion 41 controls the light source 18 of the magnetic sensor 10 to perform irradiation with irradiation light. Specifically, the irradiation control portion 41 controls not only starting or ending of irradiation with irradiation light in the light source 18 but also intensity of the irradiation light, a direction of a linear polarization plane included in the irradiation light, and the like.

The magnetic field generation control portion 42 controls the magnetic field generator 8 (8X, 8Y, and 8Z) to generate predetermined magnetic fields in the X, Y and Z axis directions, respectively. Specifically, the magnetic field generation control portion 42 causes the magnetic field generator 8 (8X, 8Y, and 8Z) to generate a predetermined artificial magnetic field A (A_(x), A_(y), A_(z)) at the initial setting. As will be described later in detail, the artificial magnetic field A is an alternating magnetic field f (ωt) in which a first direction (X direction) component and a second direction (Y direction) component thereof have the same amplitude and cycle and different phases, and is a magnetic field vector in which a third direction (Z direction) component thereof is zero (A_(z)=0). The artificial magnetic field A (A_(x), A_(y), A_(z)) is stored as artificial magnetic field data 52 in the storage unit 50.

During measurement, the magnetic field generation control portion 42 causes the magnetic field generator 8 (8X, 8Y, and 8Z) to generate a combined magnetic field (B_(b)+A) of a bias magnetic field B_(b) (B_(bx), B_(by), B_(bz)) determined by the bias magnetic field determination portion 44 and the artificial magnetic field A (A_(x), A_(y), A_(z)).

The original magnetic field calculation portion 43 calculates an original magnetic field vector C (C_(x), C_(y), C_(z)) on the basis of a signal output from the magnetic sensor 10 in a state in which the magnetic field generator 8 (8X, 8Y, and 8Z) generates the artificial magnetic field vector A (A_(x), A_(y), A_(z)). Specifically, a magnetic sensor measurement value (square difference W⁻) obtained on the basis of the signal output from the magnetic sensor 10 is set as a spin polarization degree M_(x), and three or more combinations of a value A_(x) (t) of the X axis direction component A_(x) of the artificial magnetic field vector A, a value A_(y) (t) of the Y axis direction component A_(y) thereof, and a spin polarization degree M_(x) (t) at a certain time point t and having different spin polarization degrees M_(x) are acquired.

In addition, simultaneous equations formed of three or more equations which are obtained by assigning each of the acquired combinations to Equation 15 to be described later are defined, and the original magnetic field vector C (C_(x), C_(y), C_(z)) is calculated by performing a predetermined arithmetic calculation process for solving the simultaneous equations. The calculated original magnetic field C (C_(x), C_(y), C_(z)) is stored as original magnetic field data 53 in the storage unit 50.

The bias magnetic field determination portion 44 determines the bias magnetic field B_(b) (B_(bx), B_(by), B_(bz)) which cancels out the original magnetic field vector C (C_(x), C_(y), C_(z)) calculated by the original magnetic field calculation portion 43. The determined bias magnetic field B_(b) (B_(bx), B_(by), B_(bz)) is stored as bias magnetic field data 54 in the storage unit 50.

The target magnetic field calculation portion 45 calculates a target magnetic field vector B (B_(y), B_(y), B_(z)) generated by a measurement target object on the basis of a signal output from the magnetic sensor 10 in a state in which the measurement target object is disposed and the magnetic field generator 8 generates the bias magnetic field B_(b). Specifically, a measurement value (square difference W⁻) obtained on the basis of the signal output from the magnetic sensor 10 is set as a spin polarization degree M_(x), and three or more combinations of a value A_(x)(t) of the X axis direction component A_(x) of the artificial magnetic field vector A, a value A_(y) (t) of the Y axis direction component A_(y) thereof, and a spin polarization degree M_(x)(t) at a certain time point t and having different spin polarization degrees M_(x) are acquired.

In addition, simultaneous equations formed of three or more equations which are obtained by assigning each of the acquired combinations to Equation 15 to be described later are defined, and the original magnetic field vector C (C_(x), C_(y), C_(z)) is calculated as the target magnetic field B (B_(x), B_(y), B_(z)) generated by the measurement target object by performing a predetermined arithmetic calculation process for solving the simultaneous equations. The calculated target magnetic field vector B (B_(x), B_(y), B_(z)) is stored as measured magnetic field data 55 in the storage unit 50. The magnetic sensor measurement value (square difference W⁻) obtained on the basis of a signal output from the magnetic sensor 10 is stored as magnetic sensor measurement data 56 in the storage unit 50.

The storage unit 50 is constituted of a storage device such as a read only memory (ROM), a random access memory (RAM), or a hard disk. The storage unit 50 stores a program, data, or the like for the processing unit 40 integrally controlling the calculation controller 30, and is used as a work area of the processing unit 40 so as to temporarily store results of calculation performed by the processing unit 40, operation data from the operation unit 31, or the like. In the present embodiment, the storage unit 50 stores a magnetic field measurement program 51, the artificial magnetic field data 52, the original magnetic field data 53, the bias magnetic field data 54, the measured magnetic field data 55, and the magnetic sensor measurement data 56.

Principle

A description will be made of a magnetic field measurement principle in the magnetic field measurement apparatus 1. FIG. 8 is a diagram for explaining an alignment in a case where there is no magnetic field. FIG. 9 is a diagram for explaining a change in the alignment due to a magnetic field. FIGS. 10 and 11 are diagrams for explaining a change in a polarization plane of linearly polarized light due to transmission into the gas cell. FIG. 12 is a diagram illustrating a relationship between an alignment azimuth angle θ and a detection result of probe light.

In the following description, for better understanding of the principle, the description is made in a time series, but, actually, (A) optical pumping and (C) probing may simultaneously occur in a one-beam method of the present embodiment.

(A) Optical Pumping

The gaseous alkali metal atoms enclosed in the gas cell 12 are irradiated with pump light (light passing through the gas cell 12 in the present embodiment) which is adjusted to a wavelength corresponding to a transition from a state of the hyperfine structure quantum number F to a state of F′ (=F−1) in the D1-line, and are thus brought into a group in which (spin-polarized) atoms whose spins are directed in anti-parallel directions (opposite directions) exist in substantially the same number. This state is referred to as an alignment. The spin polarization of a single atom is alleviated with the passage of time, but since the pump light is continuous wave (CW) light, formation and alleviation of spin polarization are repeatedly performed simultaneously and continuously, and, as a result, steady spin polarization is formed in terms of the entire atom group.

In a case where the measurement region 5 is a zero magnetic field, the alignment is expressed by a probability distribution of magnetic moments of the atoms. In a case where the pump light is linearly polarized light as in the present embodiment, as illustrated in FIG. 8, a shape thereof is a shape of a region R in which two ellipses growing in oscillation directions (the Y axis direction in the present embodiment) of an electric field of the linearly polarized light of the pump light are connected to each other on the X-Y plane.

(B) Action of Magnetic Field

If a certain magnetic field is present in the measurement region 5, the alkali metal atom starts to precess with a direction of a magnetic field vector (a magnetic field received by the gas cell 12) as a rotation axis. As illustrated in FIG. 9, the direction (a direction along a major axis of the ellipse) of the alignment changes so as to be rotated with the origin O as a center, due to an addition of an optical pumping action caused by the pump light and an alleviation action caused by collision of the gaseous atom into the inner wall of the gas cell 12.

The direction of the alignment is brought into a steady state in an arrangement of being rotated about the Y axis by an angle (θ) corresponding to the strength of the magnetic field. Here, an alignment direction is indicated by θp, and a direction perpendicular thereto is indicated by Os. An angle θ formed between the Y axis direction which is the oscillation direction of the electric field of the pump light and the alignment direction θp is referred to as an alignment azimuth angle θ. The alignment azimuth angle θ mainly increases according to the magnetic field strength in the Z axis direction.

(C) Probing

It is assumed that probe light (light passing through the gas cell 12 in the present embodiment) having a linearly polarized light component of which an electric field vector E₀ oscillates in the Y axis direction passes through the atom group in this state. In other words, as illustrated in FIG. 10, the linearly polarized light in which an oscillation direction of an electric field of the probe light is the Y axis direction is caused to pass through the gas cell 12 in the +Z direction. In FIG. 10, the origin O corresponds to a position of the atom group (the gaseous atoms enclosed in the gas cell 12), and the atom group is optically pumped so that the alignment occurs which is distributed in the region along the Y axis direction. In the Z axis direction, the −Z direction side shows linearly polarized light before being transmitted through the atom group, and the +Z direction shows linearly polarized light (transmitted light) after being transmitted through the atom group.

If the linearly polarized light is transmitted through the atom group, a polarization plane of the linearly polarized light is rotated due to linear dichroism, and the electric field vector changes to E₁. The linear dichroism is a property in which transmittance of the linearly polarized light differs in the direction θp (refer to FIG. 9) of the alignment and in the direction θs (refer to FIG. 9) perpendicular to the alignment. Specifically, since a component in the direction θs perpendicular to the alignment is absorbed more than a component in the direction θp of the alignment, the polarization plane of the probe light is rotated so as to become close to the direction θp of the alignment.

FIG. 11 is a diagram illustrating a state of rotation of the polarization plane before and after the linearly polarized light is transmitted through the atom group on the X-Y plane perpendicular to the Z axis direction which is an irradiation direction of the probe light. In the present embodiment, the probe light incident to the gas cell 12 is linearly polarized light of the electric field vector E₀ in which an oscillation direction of the electric field is the Y axis direction. Due to the alignment, the component in the direction θp of the probe light is transmitted with the transmittance t_(p), and the component in the direction θs is transmitted with the transmittance t_(s). Since t_(p)>t_(s) due to the linear dichroism, the polarization plane of the probe light which has been transmitted through the gas cell 12 is rotated so as to become close to the direction θp. In this way, the light having passed through the gas cell 12 has the electric field vector E₁.

Specifically, a component of the electric field vector E₀ along the alignment is indicated by E_(0P), and a component of the electric field vector E₀ perpendicular to the alignment and a traveling direction of linearly polarized light is indicated by E_(0s). A component of the electric field vector E₁ along the alignment is indicated by E_(1P), and a component of the electric field vector E₁ perpendicular to the alignment and a traveling direction of linearly polarized light is indicated by E_(1s). In this case, the following relationship is satisfied: E_(1P)=t_(p)E_(0P), and E_(1s)=t_(s)E_(0s).

If an angle (hereinafter, referred to as an “alignment azimuth angle”) formed between the direction of the alignment and the oscillation direction of the electric field of the probe light is indicated by θ, the respective components of the electric field vector E₁ in the direction θp and the direction θs are calculated using the following Equation 2 on the basis of the above-described relationship.

$\begin{matrix} {{\overset{\rightarrow}{E}}_{1} = \left( \begin{matrix} 0 & {\left. E_{0} \right)\begin{pmatrix} {\cos \; \theta} & {\sin \; \theta} \\ {{- \sin}\; \theta} & {\cos \; \theta} \end{pmatrix}\begin{pmatrix} t_{s} & 0 \\ 0 & t_{p} \end{pmatrix}} \end{matrix} \right.} & (2) \end{matrix}$

As described above, the probe light which has been transmitted through the gas cell 12 is separated into two polarized light components along an α axis which forms +45 degrees with the Y axis direction which is an irradiation direction of the probe light and a β axis which forms −45 degrees with the Y axis direction by the polarization separator 13. An α axis direction component E_(α) and a β axis direction component E_(β) of the linearly polarized light with the electric field vector E₁ which has been transmitted through the gas cell 12 are calculated according to Equation 3.

$\begin{matrix} \left( \begin{matrix} E_{\alpha} & {\left. E_{\beta \;} \right) = {{\overset{\rightarrow}{E}}_{1}\begin{pmatrix} {\cos \left( {{- \frac{\pi}{4}} - \theta} \right)} & {\sin \left( {{- \frac{\pi}{4}} - \theta} \right)} \\ {- {\sin \left( {{- \frac{\pi}{4}} - \theta} \right)}} & {\cos \left( {{- \frac{\pi}{4}} - \theta} \right)} \end{pmatrix}}} \end{matrix} \right. & (3) \end{matrix}$

The photodetectors 14 and 15 measure light intensities of the two polarized light components along the α axis and the β axis, and output signals corresponding to amounts of received light to the calculation controller 30. The calculation controller 30 processes the signals from the photodetectors 14 and 15, and calculates a square sum W₊ and a square difference W⁻ of the components in the directions along the α axis and the β axis according to Equations 4 and 5. E_(α) indicates the light intensity of the component in the α axis direction, and E_(β) indicates the light intensity of the component in the β axis direction.

W ₊ =E _(α) ² +E _(β) ²  (4)

W ⁻ =E _(α) ² −E _(β) ²  (5)

FIG. 12 illustrates the α axis direction and β axis direction components E_(α) and E_(β) of the linearly polarized light with the electric field vector E₁, square values E_(α) ² and E_(β) ² thereof, and a square sum W₊ and a square difference W⁻ of the components in the directions along the α axis and the β axis, relative to the alignment azimuth angle θ. A case where the alignment azimuth angle θ is 0 indicates that the measurement region 5 is in a zero magnetic field state (refer to FIG. 8). Here, the transmittance t_(p) of the component in the direction θp is 1, and the transmittance t_(s) of the component in the direction θs is 0.8.

In FIG. 12, looking at the value of the square difference W⁻, the square difference W⁻ oscillates in a cycle of 180 degrees with respect to the alignment azimuth angle θ. The square difference W⁻ substantially linearly changes with respect to the alignment azimuth angle θ in the range of the alignment azimuth angle θ from −45 degrees to +45 degrees, and thus high sensitivity can be obtained. Since the center of the linear change is 0 degrees, and a range of the linear change is wider than other ranges (the square sum W₊ and the like), this is suitable for measuring a magnetic field generated in the measurement region 5. Since a biomagnetic field such as a heart magnetic field or a brain magnetic field is weak, and the alignment azimuth angle θ is small, it is possible to observe a rotation angle of the polarization plane with high sensitivity using the square difference W⁻.

However, as described above, if an unnecessary magnetic field which is different from a magnetic field of a measurement target object is present in the measurement region 5, sensitivity is reduced due to an influence thereof, and thus measurement accuracy is reduced. Typically, when a magnetic field of a measurement target object, such as a heart magnetic field or a brain magnetic field is measured, the measurement is performed in an environment in which the magnetic shield device 6 prevents an external magnetic field from entering the measurement region 5 (a state in which the external magnetic field is not considerable), but it is hard to sufficiently reduce the external magnetic field to an extent of not influencing the measurement depending on the magnetic shield device 6. In other words, inmost cases, the magnetic shield device 6 cannot completely prevent the entry of the external magnetic field. A magnetic shield device which can completely shield a magnetic field is large-sized and expensive, and installation costs or operation costs thereof are high.

Therefore, in the present embodiment, the magnetic shield device 6 is used, an external magnetic field (referred to as an original magnetic field C) which enters the magnetic shield device 6 is measured, and a magnetic field of a measurement target object is measured in a state in which the external magnetic field is reduced using the magnetic field generator 8. However, in a case where the external magnetic field is originally low, or the external magnetic field is stable, the present embodiment can be implemented without using even the magnetic shield device 6.

According to FIG. 12, in the range of the alignment azimuth angle θ from −45 degrees to +45 degrees, the square difference W⁻ is substantially proportional to an X axis direction component M_(x) (hereinafter, referred to as a spin polarization degree M_(x)) of a spin polarization degree (M_(x), M_(y), M_(z)). The spin polarization degree M_(x) corresponds to a magnetization value which is an X axis direction component of a magnetization vector obtained by combining magnetic moments of atoms. For this reason, hereinafter, the square difference W⁻ is treated as the spin polarization degree M_(x). In the present embodiment, the spin polarization degree M_(x) is focused, and there is derivation of a relational expression indicating how a value of the spin polarization degree M_(x) changes according to respective components B_(x), B_(y), and B_(z) of the magnetic field vector B applied to the gas cell 12.

The time development of the spin polarization degree (M_(x), M_(y), M_(z)) of an alignment caused by optical pumping is approximated according to Bloch equations shown in the following Equations 6 to 8. γ_(F) indicates a magnetic rotation ratio which is defined depending on the kind of medium gas (alkali metal atom gas) in the gas cell 12. Γ₀ indicates alleviation speed of the spin polarization degree (M_(x), M_(y), M_(z)), and Γ_(p) indicates optical pumping speed. M_(p) indicates the maximum magnetization when spins of the alkali metal atom group are all aligned in one direction.

$\begin{matrix} {\frac{M_{x}}{t} = {{\gamma_{F}\left( {{M_{y}B_{z}} - {M_{z}B_{y}}} \right)} - {\Gamma_{0}M_{x}} - {\Gamma_{p}M_{x}}}} & (6) \\ {\frac{M_{y}}{t} = {{\gamma_{F}\left( {{M_{z}B_{x}} - {M_{x}B_{z}}} \right)} - {\Gamma_{0}M_{y}} - {\Gamma_{p}\left( {M_{p} - M_{y}} \right)}}} & (7) \\ {\frac{M_{z}}{t} = {{\gamma_{F}\left( {{M_{x}B_{y}} - {M_{y}B_{x}}} \right)} - {\Gamma_{0}M_{z}} - {\Gamma_{p}M_{z}}}} & (8) \end{matrix}$

Since pumping light and probe light are applied to the gas cell 12 with constant power in a steady state, a steady solution of the spin polarization degree (M_(x), M_(y), M_(z)) can be obtained by setting the respective left sides of the above Equations 6 to 8 to zero. The solution can be obtained according to Equations 9 to 11.

$\begin{matrix} {M_{x} = {\frac{c}{a} \cdot \frac{{B_{x}B_{y}} + {aB}_{z}}{a^{2} + B_{x}^{2} + B_{y}^{2} + B_{z}^{2}}}} & (9) \\ {M_{y} = {\frac{c}{a} \cdot \frac{a^{2} + B_{y}^{2}}{a^{2} + B_{x}^{2} + B_{y}^{2} + B_{z}^{2}}}} & (10) \\ {M_{z} = {\frac{c}{a} \cdot \frac{{B_{y}B_{z}} - {aB}_{x}}{a^{2} + B_{x}^{2} + B_{y}^{2} + B_{z}^{2}}}} & (11) \end{matrix}$

In Equations 9 to 11, a and c are constants and are given by the following Equation 12.

$\begin{matrix} {a = {{\frac{\Gamma_{0} + \Gamma_{p}}{\gamma_{F}}\mspace{14mu} c} = {\Gamma_{p}M_{p}}}} & (12) \end{matrix}$

(D) Measurement of Magnetic Field

Meanwhile, a case is assumed in which the artificial magnetic field A (A_(x), A_(y), A_(z)) is generated in the X axis direction, the Y axis direction, and the Z axis direction by the magnetic field generator 8 (8X, 8Y, and 8Z), and is applied to the gas cell 12. In this case, the magnetic field vector B (B_(x), B_(y), B_(z)) detected by the magnetic sensor 10 is a vector sum of the artificial magnetic field vector A (A_(x), A_(y), A_(z)) generated by the magnetic field generator 8 and the original magnetic field vector C (C_(x), C_(y), C_(z)) as shown in Equation 13. The original magnetic field C is a magnetic field which is present in the measurement region 5 when the artificial magnetic field A is zero.

{right arrow over (B)}={right arrow over (A)}+{right arrow over (C)}(B _(x) B _(y) B _(z))=(A _(x) +C _(x) A _(y) +C _(y) A _(z) +C _(z))  (13)

Here, the Z axis direction component A_(z) of the artificial magnetic field vector A is set to zero (A_(z)=0). The X axis direction component A_(x) of the artificial magnetic field vector A is set to an alternating magnetic field f (ωt) having the amplitude A₁₀ and a frequency ω. In other words, the X axis direction component A_(x) of the artificial magnetic field vector A is set to a first alternating magnetic field (A_(x)=A₁₀f (ωt)). In addition, the Y axis direction component A_(y) thereof is set to an alternating magnetic field f (ωt+δ) which has a phase difference δ with the first alternating magnetic field, and has the amplitude A₂₀ and a frequency ω. In other words, the Y axis direction component A_(y) of the artificial magnetic field vector A is set to a second alternating magnetic field (A_(y)=A₂₀f (ωt+δ)). The phase difference δ is not zero (δ≠0). In other words, as the artificial magnetic field A, a rotation magnetic field with the Z axis direction as an axis is superimposed on the original magnetic field C.

The alternating magnetic field f (ωt) is any periodic function satisfying f (ωt))=f (ωt+2π). In this case, the magnetic field vector B (B_(x), B_(y), B_(z)) detected by the magnetic sensor 10 in the measurement region 5 is expressed by the following Equation 14. The amplitude A₁₀ and the amplitude A₂₀ are coefficients having dimensions of magnetic fields, and the alternating magnetic field f (ωt) is a non-dimension function.

$\begin{matrix} {\begin{pmatrix} B_{x} \\ B_{y} \\ B_{z} \end{pmatrix} = \begin{pmatrix} {C_{x} + {A_{10}{f\left( {\omega \; t} \right)}}} \\ {C_{y} + {A_{20}{f\left( {{\omega \; t} + \delta} \right)}}} \\ C_{z} \end{pmatrix}} & (14) \end{matrix}$

If Equation 14 is assigned to the spin polarization degree M_(x) of Equation 9, Equation 15 can be obtained.

$\begin{matrix} {M_{x} = {\frac{c}{a} \cdot \frac{\begin{matrix} {{C_{x}C_{y}} + {C_{x}A_{20}{f\left( {{\omega \; t} + \delta} \right)}} + {C_{y}A_{10}f\left( {\omega \; t} \right)} +} \\ {{A_{10}{f\left( {\omega \; t} \right)}A_{20}{f\left( {{\omega \; t} + \delta} \right)}} + {aC}_{z}} \end{matrix}}{\begin{matrix} {a^{2} + C_{x}^{2} + C_{y}^{2} + C_{z}^{2} + {2\; C_{x}A_{10}{f\left( {\omega \; t} \right)}} +} \\ {{2\; C_{y}A_{20}{f\left( {{\omega \; t} + \delta} \right)}} + {A_{10}^{2}{f\left( {\omega \; t} \right)}^{2}} + {A_{20}^{2}{f\left( {{\omega \; t} + \delta} \right)}^{2}}} \end{matrix}}}} & (15) \end{matrix}$

If A₁₀=A₂₀=A₀, control and computation are facilitated, and Equations 14 and 15 are expressed as in the following Equations 16 and 17.

$\begin{matrix} {\begin{pmatrix} B_{x} \\ B_{y} \\ B_{z} \end{pmatrix} = \begin{pmatrix} {C_{x} + {A_{0}{f\left( {\omega \; t} \right)}}} \\ {C_{y} + {A_{0}{f\left( {{\omega \; t} + \delta} \right)}}} \\ C_{z} \end{pmatrix}} & (16) \\ {M_{x} = {\frac{c}{a} \cdot \frac{\begin{matrix} {{C_{x}C_{y}} + {C_{x}A_{0}f\left( {{\omega \; t} + \delta} \right)} + {C_{y}A_{0}{f\left( {\omega \; t} \right)}} +} \\ {{A_{0}^{2}{f\left( {\omega \; t} \right)}{f\left( {{\omega \; t} + \delta} \right)}} + {aC}_{z}} \end{matrix}}{\begin{matrix} {a^{2} + C_{x}^{2} + C_{y}^{2} + C_{z}^{2} + {2\; C_{x}A_{0}{f\left( {\omega \; t} \right)}} +} \\ {{2\; C_{y}A_{0}{f\left( {{\omega \; t} + \delta} \right)}} + {A_{0}^{2}\left( {{f\left( {\omega \; t} \right)}^{2} + {f\left( {{\omega \; t} + \delta} \right)}^{2}} \right)}} \end{matrix}}}} & (17) \end{matrix}$

Three values of the respective components (C_(x), C_(y), C_(z)) of the original magnetic field vector C which are the unknowns are calculated as follows using Equation 15 or Equation 17. That is, the magnetic field measurement apparatus 1 causes the magnetic field generator 8 to generate the artificial magnetic field A (t) having the X axis direction component A_(x) (t) and the Y axis direction component A_(y) (t) at a certain time point t, and measures the spin polarization degree M_(x) (t) (that is, the square difference W⁻(t)) at this time. Three or more spin polarization degree M_(x) (t) are acquired by taking three or more different combinations of X axis direction components A_(x) (t) (first alternating magnetic field) and Y axis direction components A_(y) (t) (second alternating magnetic field).

In addition, simultaneous equations defined by three equations which are obtained by assigning the values A_(x) (t) and A_(y) (t) of the artificial magnetic field A and the spin polarization degree M_(x)(t) to Equation 15 or Equation 17 are generated for each combination. It is possible to calculate the respective components (C_(x), C_(y), C_(z)) of the original magnetic field vector C which are the unknowns by solving the simultaneous equations.

In Equation 15 or 17, the constants a and c may be the unknowns. In other words, Equation 15 or 17 contains five unknowns including the respective components (C_(x), C_(y), C_(z)) of the original magnetic field vector C, and the constants a and c. In this case, measurement is performed using the magnetic field measurement apparatus 1, and five combinations of the artificial magnetic fields A_(x)(t) and A_(y)(t) and the spin polarization degree M_(x) (t) at a certain time point t and having different spin polarization degrees M_(x) (t) are acquired. In addition, simultaneous equations defined by five equations which are obtained by assigning the respective values to Equation 17 are generated for each combination. It is possible to calculate the respective components (C_(x), C_(y), C_(z)) of the original magnetic field vector C, and the constants a and c, which are the unknowns by solving the simultaneous equations.

Further, six or more combinations of the artificial magnetic fields A_(x) (t) and A_(y) (t) and the spin polarization degree M_(x) (t) and having different spin polarization degrees M_(x) (t) may be acquired, and Equation 17 may be fitted to the combinations. Specifically, the respective components (C_(x), C_(y), C_(z)) of the original magnetic field vector C, and the constants a and c, which are the unknowns, are calculated so that a deviation between the spin polarization degree M_(x) calculated using Equation 17 and the measured value M_(x) of the magnetic sensor 10 becomes the minimum.

If the alternating magnetic field f(ωt) set as the artificial magnetic fields A_(x) and A_(y) employs a periodic function expressed by the following Equation 18, Equation 17 is simplified as Equation 19, and thus measurement is more easily performed.

$\begin{matrix} {{{f\left( {\omega \; t} \right)}^{2} + {f\left( {{\omega \; t} + \delta} \right)}^{2}} = {{const} = K^{2}}} & (18) \\ {M_{x} = {\frac{c}{a} \cdot \frac{\begin{matrix} {{C_{x}C_{y}} + {C_{x}A_{0}f\left( {{\omega \; t} + \delta} \right)} +} \\ {{C_{y}A_{0}{f\left( {\omega \; t} \right)}} + {A_{0}^{2}{f\left( {\omega \; t} \right)}{f\left( {{\omega \; t} + \delta}\; \right)}} + {aC}_{z}} \end{matrix}}{\begin{matrix} {a^{2} + C_{x}^{2} + C_{y}^{2} + C_{z}^{2} + {2\; C_{x}A_{0}f\left( {\omega \; t} \right)} +} \\ {{2\; C_{y}A_{0}{f\left( {{\omega \; t} + \delta} \right)}} + {A_{0}^{2}K^{2}}} \end{matrix}}}} & (19) \end{matrix}$

If the amplitude A₀ of the alternating magnetic field f(ωt) is sufficiently smaller than the X axis direction component C_(x) and the Y axis direction component C_(y) of the original magnetic field C (generally, 1/10 or less; A₀<(C_(x)/10) and A₀<(C_(y)/10)), Equations 17 and 19 are simplified as Equation 20, and thus measurement is more easily performed.

                                          (20) $M_{x} = {\frac{c}{a} \cdot \frac{{C_{x}C_{y}} + {C_{x}A_{0}{f\left( {{\omega \; t} + \delta} \right)}} + {C_{y}A_{0}f\left( {\omega \; t} \right)} + {aC}_{z}}{a^{2} + C_{x}^{2} + C_{y}^{2} + C_{z}^{2} + {2\; C_{x}A_{0}{f\left( {\omega \; t} \right)}} + {2\; C_{y}A_{0}{f\left( {{\omega \; t} + \delta} \right)}}}}$

As mentioned above, the original magnetic field vector C (C_(x), C_(y), C_(z)) can be calculated on the basis of the artificial magnetic field A (A_(x), A_(y), A_(z)) generated by the magnetic field generator 8 and the spin polarization degree M_(x) (that is, the square difference W⁻) at that time using Equation 15, 17, 19 or 20.

Flow of Process

FIG. 13 is a flowchart illustrating a flow of a magnetic field measurement process according to the present embodiment. This process is a process which is realized by each portion of the processing unit 40 illustrated in FIG. 7 executing the magnetic field measurement program 51. As an example, a description will be made of a case where a measurement target object is the human body (subject 9), and a heart magnetic field (a magnetic field generated due to an electrophysiological activity of the heart) or a brain magnetic field is measured.

As illustrated in FIG. 13, first, the irradiation control portion 41 causes the light source 18 to start irradiation with irradiation light including linearly polarized light components which serve as pump light and probe light (step S01). Thereafter, in order to measure the original magnetic field C, the magnetic field generation control portion 42 causes the magnetic field generator 8 (8X, 8Y, and 8Z) to generate the artificial magnetic field A (A_(x), A_(y), A_(z)) (step S02).

Next, the original magnetic field calculation portion 43 acquires combinations of measurement values (square differences W⁻) obtained on the basis of signals output from the magnetic sensor 10 at three or more different timings t and values of the artificial magnetic fields A_(x) and A_(y) at the timings in a state in which the artificial magnetic field A is generated (step S03). The original magnetic field calculation portion 43 calculates the original magnetic field vector C (C_(x), C_(y), C_(z)) using the acquired combinations of the measurement values (square differences W⁻) and the artificial magnetic fields A_(x) and A_(y) (step S04).

Next, the bias magnetic field determination portion 44 determines the bias magnetic field B_(b) (B_(bx), B_(by), B_(bz)) which cancels out the calculated original magnetic field C (step S05). Next, the measurement target object (subject 9) is disposed to be close to the magnetic sensor 10 in the magnetic shield device 6 (measurement region 5) (step S06).

Next, in order to measure the magnetic field B generated by the measurement target object (subject 9), the magnetic field generation control portion 42 causes the magnetic field generator 8 (8X, 8Y, and 8Z) to generate a combined magnetic field of the bias magnetic field B_(b) and the artificial magnetic field A (step S07).

Thereafter, the target magnetic field calculation portion 45 acquires combinations of measurement values (square differences W⁻) obtained on the basis of signals output from the magnetic sensor 10 at three or more different timings t and values of the artificial magnetic fields A_(x) and A_(y) at the timings in a state in which the combined magnetic field is generated (step S08). The target magnetic field calculation portion 45 calculates the target magnetic field B (B_(x), B_(y), B_(z)) generated by the measurement target object using the acquired combinations of the measurement values (square differences W⁻) and the artificial magnetic fields A_(x) and A_(y) (step S09).

Thereafter, the irradiation control portion 41 causes the light source 18 to finish the irradiation with the irradiation light (step S10). If the above-described processes are performed, the processing unit 40 finishes the magnetism measurement process.

As specific Examples in the magnetic field measurement apparatus 1 with the above-described configuration, four Examples for specifically describing the artificial magnetic field A (A_(x), A_(y), A_(z)) will now be described.

Example 1

Example 1 is an example in which the alternating magnetic field f(ωt) set as the X axis direction component A_(x) and the Y axis direction component A_(y) of the artificial magnetic field A employs a trigonometric function wave, and has the phase difference δ of “π/2”. In other words, the artificial magnetic field vector A (A_(x), A_(y), A_(z)) is expressed as in the following Equation 21.

$\begin{matrix} {\overset{\rightarrow}{A} = {\begin{pmatrix} A_{x} \\ A_{y} \\ A_{z} \end{pmatrix} = {\begin{pmatrix} {f\left( {\omega \; t} \right)} \\ {f\left( {{\omega \; t} + \delta} \right)} \\ 0 \end{pmatrix} = {\begin{pmatrix} {A_{0}{\cos \left( {\omega \; t} \right)}} \\ {A_{0}{\cos \left( {{\omega \; t} - \frac{\pi}{2}} \right)}} \\ 0 \end{pmatrix} = \begin{pmatrix} {A_{0}{\cos \left( {\omega \; t} \right)}} \\ {A_{0}{\sin \left( {\omega \; t} \right)}} \\ 0 \end{pmatrix}}}}} & (21) \end{matrix}$

Therefore, the magnetic field B applied to the gas cell 12 is expressed by the following Equation 22.

$\begin{matrix} {\begin{pmatrix} B_{x} \\ B_{y} \\ B_{z} \end{pmatrix} = {\begin{pmatrix} {A_{x} + C_{x}} \\ {A_{y} + C_{y}} \\ {A_{z} + C_{z}} \end{pmatrix} = \begin{pmatrix} {{A_{0}{\cos \left( {\omega \; t} \right)}} + C_{x}} \\ {{A_{0}{\sin \left( {\omega \; t} \right)}} + C_{y}} \\ C_{z} \end{pmatrix}}} & (22) \end{matrix}$

Equation 15 related to the spin polarization degree M_(x) is expressed as in the following Equation 23.

                                          (23) $M_{x} = {\frac{c}{a} \cdot \frac{{C_{x}C_{y}} + {C_{x}A_{0}{\sin \left( {\omega \; t} \right)}} + {C_{y}A_{0}{\cos \left( {\omega \; t} \right)}} + {A_{0}^{2}{\sin \left( {\omega \; t} \right)}{\cos \left( {\omega \; t} \right)}} + {aC}_{z}}{a^{2} + C_{x}^{2} + C_{y}^{2} + C_{z}^{2} + {2\; C_{x}A_{0}{\cos \left( {\omega \; t} \right)}} + {2\; C_{y}A_{0}{\sin \left( {\omega \; t} \right)}} + A_{0}^{2}}}$

If the amplitude A₀ of the alternating magnetic field f(ωt) is sufficiently smaller than the X axis direction component C_(x) and the Y axis direction component C_(y) of the original magnetic field C (generally, 1/10 or less; A₀<(C_(x)/10) and A₀<(C_(y)/10)), Equation 23 is simplified as Equation 24.

$\begin{matrix} {M_{x} = {\frac{c}{a} \cdot \frac{{C_{x}C_{y}} + {C_{x}A_{0}{\sin \left( {\omega \; t} \right)}} + {C_{y}A_{0}\cos \left( {\omega \; t} \right)} + {aC}_{z}}{a^{2} + C_{x}^{2} + C_{y}^{2} + C_{z}^{2} + {2\; C_{x}A_{0}{\cos \left( {\omega \; t} \right)}} + {2\; C_{y}A_{0}{\sin \left( {\omega \; t} \right)}}}}} & (24) \end{matrix}$

In addition, measurement is performed using the magnetic field measurement apparatus 1, and three or more artificial magnetic fields having different combinations of the X axis direction component A_(x)(t) and the Y axis direction component A_(y)(t) are formed, and the spin polarization degrees M_(x)(t) (that is, the square difference W⁻) at that time are acquired. In other words, a magnetization value M_(x)(t_(i)) is acquired in a state in which an artificial magnetic field A_(i) having an X axis direction component A_(x)(t_(i)) and a Y axis direction component A_(y) (t_(i)) is formed in the measurement region. Here, i is any integer from 1 to n, and n is an integer of 3 or greater.

In a case where j is set to any integer of 1 to n so as to be different from i, a case where “combinations of the X axis direction component A_(x)(t) and the Y axis direction component A_(y)(t) are different from each other” satisfies at least one of a case where an X axis direction component A_(x)(t_(i)) at a time point t_(i) is different from an X axis direction component A_(x)(t_(j)) at a time point t_(j) (A_(x)(t_(i))≠A_(x)(t_(j))), and a case where a Y axis direction component A_(y) (t_(i)) at the time point t_(i) is different from a Y axis direction component A_(y)(t_(j)) at the time point t_(j) (A_(y) (t_(i))≠A_(y) (t_(j))).

In addition, simultaneous equations defined by three or more equations which are obtained by assigning the values A_(x)(t) and A_(y) (t) of the artificial magnetic field and the spin polarization degree M_(x)(t) to Equation 23 are generated for each combination, and it is possible to calculate the respective components (C_(x), C_(y), C_(z)) of the original magnetic field vector C which are the unknowns by solving the simultaneous equations.

FIG. 14 shows graphs illustrating examples of the artificial magnetic fields A_(x) and A_(y) and the spin polarization degree M_(x) in Example 1. FIG. 14 shows graphs of the artificial magnetic fields A_(x) and A_(y) corresponding to one cycle (2π) and the spin polarization degree M_(x), in which transverse axes thereof express a phase ωt. The lower drawing vertically enlarges and illustrates a part of the upper graph for better understanding of a change in the spin polarization degree M_(x).

As illustrated in FIG. 14, in a case where the artificial magnetic fields A_(x) and A_(y) have a trigonometric function wave, the spin polarization degree M_(x) shows a curve which smoothly changes. In other words, in one cycle period of the alternating magnetic field f (ωt), it is possible to acquire three or more combinations of the artificial magnetic fields A_(x) and A_(y) and the spin polarization degrees M_(x), which are necessary to calculate the original magnetic field vector C (C_(x), C_(y), C_(z)) using Equation 24, and having different spin polarization degrees N.

Generally, a is set to be sufficiently greater than A₀, C_(x), or C_(y) (a>10×A₀, a>10×C_(x), or a>10×C_(y)). In this case, since an oscillation term of the denominator becomes smaller, the spin polarization degree M_(x) which is a magnetization value is proportional to the numerator, and thus Equation 24 is expressed as in the following Equation 25.

M _(x) ≈C _(x) C _(y) +C _(x) A ₀ sin(ωt)+C _(y) A ₀ cos(ωt)+aC _(z)  (25)

In other words, this leads to a waveform in which a modulation signal “C_(x)A₀ sin (ωt)+C_(y)A₀ cos (ωt)” is superimposed on an output signal “C_(x)C_(y)+aC_(z)” obtained when a magnetic field modulation is not performed. If the spin polarization degree M_(x) as an output signal and a reference signal synchronized with the modulated magnetic field are input to a lock-in amplifier, two phase components “C_(x)A₀” and “C_(y)A₀” perpendicular to each other are respectively output as an in-phase signal and a quadrature signal. Since A₀ is known, the X axis direction component C_(x) and the Y axis direction component C_(y) of the original magnetic field vector C can be detected from the two signals. In the above-described manner, the X axis direction component C_(x) and the Y axis direction component C_(y) of the original magnetic field vector C may be detected.

In addition, since the magnetic sensor 10 may have a primary delay element, in a case where phase delay or a gain change occurs, a measurement condition or a measurement value may be corrected by specifying a delay phase or a gain at a frequency ω in advance. The frequency ω may be set to frequencies other than a band which is necessary in magnetic field measurement, and may be set to, for example, a cutoff frequency ω_(C) or higher. The cutoff frequency ω_(C) is a sum of alleviation speed Γ₀ of the spin polarization degree and optical pumping speed Γ_(P) (ω_(C)=Γ₀+Γ_(P)).

Example 2

Example 2 is an example in which the alternating magnetic field f (ωt) set as the X axis direction component A_(x) and the Y axis direction component A_(y) of the artificial magnetic field A employs a triangular wave, and has the phase difference δ of “π/2”.

FIG. 15 shows graphs illustrating examples of the artificial magnetic fields A_(x) and A_(y) and the spin polarization degree M_(x) in Example 2. FIG. 15 shows graphs of the artificial magnetic fields A_(x) and A_(y) corresponding to one cycle (2π) and the spin polarization degree M_(x), in which transverse axes thereof express a phase ωt. The lower drawing vertically enlarges and illustrates a part of the upper graph for better understanding of a change in the spin polarization degree M_(x).

As illustrated in FIG. 15, in a case where the artificial magnetic fields A_(x) and A_(y) have a triangular wave, the spin polarization degree M_(x) linearly changes, and a slope thereof changes at the vertexes of the triangular waves of the artificial magnetic fields A_(x) and A_(y). In other words, in one cycle period of the alternating magnetic field f (ωt), it is possible to acquire three or more combinations of the artificial magnetic fields A_(x) and A_(y) and the spin polarization degrees M_(x), which are necessary to calculate the original magnetic field vector C (C_(x), C_(y), C_(z)) using Equation 17, and having different spin polarization degrees M_(x).

Example 3

Example 3 is an example in which the alternating magnetic field f (ωt) set as the X axis direction component A_(x) and the Y axis direction component A_(y) of the artificial magnetic field A employs a sawtooth wave, and has the phase difference δ of “π”.

FIG. 16 shows graphs illustrating examples of the artificial magnetic fields A_(x) and A_(y) and the spin polarization degree M_(x) in Example 3. FIG. 16 shows graphs of the artificial magnetic fields A_(x) and A_(y) corresponding to two cycles (4π) and the spin polarization degree M_(x), in which transverse axes thereof express a phase ωt. The lower drawing vertically enlarges and illustrates a part of the upper graph for better understanding of a change in the spin polarization degree M_(x).

As illustrated in FIG. 16, in a case where the artificial magnetic fields A_(x) and A_(y) have a sawtooth wave, the spin polarization degree M_(x) linearly changes, and a slope thereof changes at the vertexes of the sawtooth waves of the artificial magnetic fields A_(x) and A_(y). In other words, in one cycle period of the alternating magnetic field f (ωt), it is possible to acquire three or more combinations of the artificial magnetic fields A_(x) and A_(y) and the spin polarization degrees M_(x), which are necessary to calculate the original magnetic field vector C (C_(x), C_(y), C_(z)) using Equation 17, and having different spin polarization degrees M_(x).

Example 4

Example 4 is an example in which the alternating magnetic field f (ωt) set as the X axis direction component A_(x) and the Y axis direction component A_(y) of the artificial magnetic field A employs a rectangular wave, and has the phase difference δ of “π/2”.

FIG. 17 shows graphs illustrating examples of the artificial magnetic fields A_(x) and A_(y) and the spin polarization degree M_(x) in Example 4. FIG. 17 shows graphs of the artificial magnetic fields A_(x) and A_(y) corresponding to one cycle and the spin polarization degree M_(x) in this order from the top, in which transverse axes thereof express a phase ωt.

As illustrated in FIG. 17, each of the artificial magnetic fields A_(x) and A_(y) takes two values (0 and A₀). The spin polarization degree M_(x) takes four values (M_(x1) to M_(x4)) corresponding to combinations of the artificial magnetic fields A_(x) and A_(y). In other words, in one cycle period of the alternating magnetic field f(ωt), it is possible to acquire three or more combinations of the artificial magnetic fields A_(x) and A_(y) and the spin polarization degrees M_(x), which are necessary to calculate the original magnetic field vector C (C_(x), C_(y), C_(z)) using Equation 17, and having different spin polarization degrees M_(x).

Specifically, in a first period τ1 in which the artificial magnetic fields A_(x)=0 and A_(y)=0, Equation 14 related to the magnetic field B applied to the magnetic sensor 10 is expressed as in the following Equation 26.

$\begin{matrix} {\begin{pmatrix} B_{x} \\ B_{y} \\ B_{z} \end{pmatrix} = \begin{pmatrix} C_{x} \\ C_{y} \\ C_{z} \end{pmatrix}} & (26) \end{matrix}$

Equation 17 related to the spin polarization degree M_(x) is expressed as in the following Equation 27.

$\begin{matrix} {M_{x\; 1} = {\frac{c}{a} \cdot \frac{{C_{x}C_{y}} + {aC}_{z}}{a^{2} + C_{x}^{2} + C_{y}^{2} + C_{z}^{2}}}} & (27) \end{matrix}$

In addition, in a second period τ2 in which the artificial magnetic field A_(x)=A₀, Equation 14 related to the magnetic field B applied to the magnetic sensor 10 is expressed as in the following Equation 28.

$\begin{matrix} {\begin{pmatrix} B_{x} \\ B_{y} \\ B_{z} \end{pmatrix} = \begin{pmatrix} {C_{x} + A_{0}} \\ C_{y} \\ C_{z} \end{pmatrix}} & (28) \end{matrix}$

Equation 17 related to the spin polarization degree M_(x) is expressed as in the following Equation 29.

$\begin{matrix} {M_{x\; 2} = {\frac{c}{a} \cdot \frac{{C_{x}C_{y}} + {C_{y}A_{0}} + {aC}_{z}}{a^{2} + C_{x}^{2} + C_{y}^{2} + C_{z}^{2} + {2\; C_{x}A_{0}} + A_{0}^{2}}}} & (29) \end{matrix}$

In a third period τ3 in which the artificial magnetic fields A_(x)=0 and A_(y)=A₀, Equation 14 related to the magnetic field B applied to the magnetic sensor 10 is expressed as in the following Equation 30.

$\begin{matrix} {\begin{pmatrix} B_{x} \\ B_{y} \\ B_{z} \end{pmatrix} = \begin{pmatrix} C_{x} \\ {C_{y} + A_{0}} \\ C_{z} \end{pmatrix}} & (30) \end{matrix}$

Equation 17 related to the spin polarization degree M_(x) is expressed as in the following Equation 31.

$\begin{matrix} {M_{x\; 3} = {\frac{c}{a} \cdot \frac{{C_{x}C_{y}} + {C_{x}A_{0}} + {aC}_{z}}{a^{2} + C_{x}^{2} + C_{y}^{2} + C_{z}^{2} + {2\; C_{y}A_{0}} + A_{0}^{2}}}} & (31) \end{matrix}$

In a fourth period τ4 in which the artificial magnetic fields A_(x)=A_(y)=0, Equation 14 related to the magnetic field B applied to the magnetic sensor 10 is expressed as in the following Equation 32.

$\begin{matrix} {\begin{pmatrix} B_{x} \\ B_{y} \\ B_{z} \end{pmatrix} = \begin{pmatrix} {C_{x} + A_{0}} \\ {C_{y} + A_{0}} \\ C_{z} \end{pmatrix}} & (32) \end{matrix}$

Equation 17 related to the spin polarization degree M_(x) is expressed as in the following Equation 33.

$\begin{matrix} {M_{x\; 4} = {\frac{c}{a} \cdot \frac{{C_{x}C_{y}} + {C_{x}A_{0}} + {C_{y}A_{0}} + A_{0}^{2} + {aC}_{z}}{a^{2} + C_{x}^{2} + C_{y}^{2} + C_{z}^{2} + {2\; C_{x}A_{0}} + {2C_{y}A_{0}} + {2A_{0}^{2}}}}} & (33) \end{matrix}$

A first equation is obtained by assigning the magnetization value (M_(x1)) obtained from the magnetic field measurement apparatus 1 in the first measurement period τ1 to the left side of Equation 27. A second equation is obtained by assigning the magnetization value (M_(x2)) obtained from the magnetic field measurement apparatus 1 in the second measurement period τ2 to the left side of Equation 29. A third equation is obtained by assigning the magnetization value (M_(x3)) obtained from the magnetic field measurement apparatus 1 in the third measurement period τ3 to the left side of Equation 31. A fourth equation is obtained by assigning the magnetization value (M_(x4)) obtained from the magnetic field measurement apparatus 1 in the fourth measurement period τ4 to the left side of Equation 33. In addition, simultaneous equations containing the four equations are solved in order to calculate the original magnetic field vector C (C_(x), C_(y), C_(z)) as the unknowns.

Example 5

Example 5 is an example in which a predetermined magnetic field is formed in the measurement region 5 instead of bring the measurement region 5 in which a measurement target object is not placed into a zero magnetic field state as in the above Examples. A magnetic field which is desired to be formed in the measurement region 5 in which a measurement target object is not placed is referred to as a target magnetic field. If the target magnetic field is desired to be formed as not a zero magnetic field but a predetermined magnetic field, combinations of the measurement value (the square difference W⁻) obtained on the basis of a signal output from the magnetic sensor 10 and values of the artificial magnetic field A_(x) and A_(y) are acquired in step S03 illustrated in FIG. 13, and then the following process is performed.

As a first procedure, a magnetic field of the measurement region 5 is calculated as the original magnetic field C using the acquired combinations of the acquired measurement value (the square difference W⁻) and the artificial magnetic field A_(x) and A_(y) (corresponding to step S04). Next, as a second procedure, a measurement target object (subject 9) is disposed in the measurement region 5 (corresponding to step S06). In Example 5, since the target magnetic field is formed not as a zero magnetic field but a predetermined magnetic field, applying (step S05 and step S07) the bias magnetic field B_(b) which cancels out the calculated original magnetic field C to the measurement region 5 is not performed.

Next, as a third procedure, a magnetic field corresponding to a difference between the target magnetic field which is a predetermined magnetic field desired to be formed in the measurement region 5 and the original magnetic field C is generated by the first magnetic field generators 8X, the second magnetic field generators 8Y, and the third magnetic field generators 8Z (corresponding to step S07). Consequently, the artificial magnetic fields A applied by the magnetic field generator 8 (8X, 8Y, and 8Z) and the original magnetic field C are combined with each other, and thus a predetermined magnetic field as the target magnetic field can be formed in the measurement region 5. The order of the second procedure and the third procedure may be changed.

In addition, as a fourth procedure, in a period in which the third procedure is being executed and the second procedure is completed, the magnetic field B generated by the measurement target object is measured using a measurement value (the square difference W⁻) obtained on the basis of a signal output from the magnetic sensor 10 (corresponding to step S09). Consequently, the magnetic field B generated by the measurement target object can be measured in a state in which the predetermined target magnetic field is formed in the measurement region 5.

In Example 5, if the target magnetic field is set to a zero magnetic field in order to cancel out the original magnetic field C which enters the measurement region 5 from the outside, it is possible to accurately measure the magnetic field B (strictly, a Z direction component of the magnetic field) generated by the measurement target object.

Example 6

Example 6 is an example in which a magnetic field of a predetermined three-dimensional vector is formed as the target magnetic field in the measurement region 5 compared with Example 5. In Example 6, a first procedure and a second procedure are the same as in Example 5.

As a third procedure, the first magnetic field generators 8X generate a third alternating magnetic field in which an X direction component of a magnetic field corresponding to a difference between the target magnetic field as a predetermined magnetic field formed in the measurement region 5 and the original magnetic field C (C_(x), C_(y), C_(z)) is added to the first alternating magnetic field, the second magnetic field generators 8Y generate a fourth alternating magnetic field in which a Y direction component of the magnetic field corresponding to the difference is added to the second alternating magnetic field, and the third magnetic field generators 8Z generate a magnetic field having a Z direction component of the magnetic field corresponding to the difference (corresponding to step S07). Consequently, the artificial magnetic field A (A_(x), A_(y), A_(z)) applied by the magnetic field generator 8 (8X, 8Y, and 8Z) and the original magnetic field vector C (C_(x), C_(y), C_(z)) are combined with each other, and thus a magnetic field of a predetermined three-dimensional vector can be formed as the target magnetic field in the measurement region 5. The order of the second procedure and the third procedure may be changed.

In addition, as a fourth procedure, in a period in which the third procedure is being executed and the second procedure is completed, the magnetic field B (B_(y), B_(y), B_(z)) generated by the measurement target object is measured using a measurement value (the square difference W⁻) obtained on the basis of a signal output from the magnetic sensor 10, the third alternating magnetic field, and the fourth alternating magnetic field (corresponding to step S09). Consequently, the magnetic field B generated by the measurement target object can be measured in a state in which the target magnetic field of a predetermined three-dimensional vector is formed in the measurement region 5.

In Example 6, if the target magnetic field is set to a zero magnetic field in order to cancel out the original magnetic field C (C_(x), C_(y), C_(z)) which enters the measurement region 5 from the outside, it is possible to accurately measure the magnetic field B generated by the measurement target object as a vector quantity.

Operations and Effects

As described above, according to the magnetic field measurement apparatus 1 of the present embodiment, the gas cell 12 in which a gas of an alkali metal atom or the like is enclosed is irradiated with irradiation light (probe light) in one direction (Z axis direction), and thus it is possible to calculate the magnetic field vector (C_(x), C_(y), C_(z)) of the measurement region.

Specifically, the artificial magnetic fields A (A_(x), A_(y), A_(z)) as the alternating magnetic fields f(ωt) which have the same cycle and different phases are applied in each of the X axis and Y axis directions perpendicular to an irradiation direction (Z axis direction) of the irradiation light (probe light). In addition, three or more combinations of the X axis direction component A_(x) and the Y axis direction component A_(y) of the artificial magnetic field A, and spin polarization degrees M_(x) corresponding to a measurement value (square difference W⁻) obtained on the basis of a signal output from the magnetic sensor 10, and having different spin polarization degrees M_(x), are acquired. The magnetic field C (C_(x), C_(y), C_(z)) is calculated using the combinations, and Equation 17 which is a relational expression among the spin polarization degrees M_(x), the respective components C_(x), C_(y), and C_(z) of the magnetic field C, and f (ωt) which is the artificial magnetic fields A_(x) and A_(y).

Modification Examples

Embodiments to which the invention is applicable are not limited to the above-described embodiment, and the embodiment may be modified as appropriate within the scope without departing from the spirit of the invention.

(A) Bias Magnetic Field B_(b)

In the above-described embodiment, the bias magnetic field B_(b) which cancels out the original magnetic field C is generated by the magnetic field generator 8, and the magnetic field B (B_(x), B_(y), B_(z)) generated by the measurement target object is measured, but measurement may be performed without generating the bias magnetic field B_(b). Specifically, first, in the same manner as in the above-described embodiment, the original magnetic field C_(x) is measured in a state in which the measurement target object is not placed. Thereafter, the measurement target object is made to be close to the magnetic sensor 10, and a magnetic field generated by the measurement target object is measured, but, at this time, only the artificial magnetic field A is generated by the magnetic field generator 8. In this case, a magnetic field applied to the measurement region is a combined magnetic field of the original magnetic field C, the magnetic field B from the measurement target object, and the artificial magnetic field A generated by the magnetic field generator 8. Therefore, a magnetic field obtained by subtracting the original magnetic field C_(x) which is measured in advance from the magnetic field C_(x) which is calculated using Equation 17 is the magnetic field B generated by the measurement target object.

(B) Measurement Target Object

In the above-described embodiment, the measurement target object is the human body, and a magnetic field (heart magnetic field) from the heart or a magnetic field (brain magnetic field) from the brain is measured, but the measurement target object may be other objects. In addition, depending on a measurement target object, instead of causing the measurement target object to be close to the magnetic sensor 10 as in the above-described embodiment, the magnetic sensor 10 may be caused to be close to the measurement target object, and a magnetic field generated by the measurement target object may be measured.

The entire disclosure of Japanese Patent Applications No. 2014-243866, filed Dec. 2, 2014 and No. 2015-154818, filed Aug. 5, 2015 are expressly incorporated by reference herein. 

What is claimed is:
 1. A magnetic field measurement method of measuring a magnetic field of a measurement region in a magnetic field measurement apparatus in which a first direction, a second direction, and a third direction are perpendicular to each other and which includes a light source that emits light, a medium through which the light passes in the third direction and that changes optical characteristics depending on a magnetic field of the measurement region, a photodetector that detects the optical characteristics, a first magnetic field generator that applies a magnetic field in the first direction to the medium, and a second magnetic field generator that applies a magnetic field in the second direction to the medium, the method comprising: causing the first magnetic field generator to generate a first alternating magnetic field; causing the second magnetic field generator to generate a second alternating magnetic field which has the same cycle as a cycle of the first alternating magnetic field and has δ as a phase difference relative to the first alternating magnetic field; and calculating the magnetic field of the measurement region using a detection result from the photodetector, the first alternating magnetic field, and the second alternating magnetic field.
 2. The magnetic field measurement method according to claim 1, wherein the calculating of the magnetic field of the measurement region includes calculating a magnetization value indicating a component in the first direction of a magnetization vector of the medium when the first alternating magnetic field and the second alternating magnetic field are generated, or a value corresponding to the magnetization value, on the basis of the detection result from the photodetector.
 3. The magnetic field measurement method according to claim 2, wherein the calculating of the magnetic field of the measurement region is performed using three or more different combinations of the first alternating magnetic field and the second alternating magnetic field.
 4. The magnetic field measurement method according to claim 3, wherein the calculating of the magnetic field of the measurement region is performed by applying the following Equation 1 to each of the combinations: $\begin{matrix} {M_{x} = {\frac{c}{a} \cdot \frac{\begin{matrix} {{C_{x}C_{y}} + {C_{x}A_{20}{f\left( {{\omega \; t} + \delta} \right)}} + {C_{y}A_{10}f\left( {\omega \; t} \right)} +} \\ {{A_{10}{f\left( {\omega \; t} \right)}A_{20}{f\left( {{\omega \; t} + \delta} \right)}} + {a\; C_{z}}} \end{matrix}}{\begin{matrix} {a^{2} + C_{x}^{2} + C_{y}^{2} + C_{z}^{2} + {2C_{x}A_{10}{f\left( {\omega \; t} \right)}} +} \\ {{2\; C_{y}A_{20}{f\left( {{\omega \; t} + \delta} \right)}} + {A_{10}^{2}{f\left( {\omega \; t} \right)}^{2}} + {A_{20}^{2}{f\left( {{\omega \; t} + \delta} \right)}^{2}}} \end{matrix}}}} & (1) \end{matrix}$ in the equation, the magnetic field of the measurement region is expressed by C=(C_(x), C_(y), C_(z)); x, y, and z respectively indicate spatial coordinates in the first direction, the second direction, and the third direction; M_(x) indicates the magnetization value; a and c are constants; A₁₀f (ωt) indicates the first alternating magnetic field; and A₂₀f (ωt+δ) indicates the second alternating magnetic field, in which δ is the phase difference, ω is an angular frequency of the first alternating magnetic field and the second alternating magnetic field, and t is time.
 5. The magnetic field measurement method according to claim 1, wherein the phase difference is π/2.
 6. The magnetic field measurement method according to claim 1, wherein the first alternating magnetic field and the second alternating magnetic field comprise trigonometric function waves.
 7. The magnetic field measurement method according to claim 1, wherein the first alternating magnetic field and the second alternating magnetic field comprise triangular waves.
 8. The magnetic field measurement method according to claim 1, wherein the first alternating magnetic field and the second alternating magnetic field comprise rectangular waves.
 9. A magnetic field measurement method of measuring a magnetic field of a measurement region in a magnetic field measurement apparatus in which a first direction, a second direction, and a third direction are perpendicular to each other and which includes a light source that emits light, a medium through which the light passes in the third direction and that changes optical characteristics depending on a magnetic field of the measurement region, a photodetector that detects the optical characteristics, a first magnetic field generator that applies a magnetic field in the first direction to the medium, a second magnetic field generator that applies a magnetic field in the second direction to the medium, and a third magnetic field generator that applies a magnetic field in the third direction to the medium, the method comprising: causing the first magnetic field generator to generate a first alternating magnetic field; causing the second magnetic field generator to generate a second alternating magnetic field which has the same cycle as a cycle of the first alternating magnetic field and has δ as a phase difference relative to the first alternating magnetic field; a first procedure of calculating the magnetic field of the measurement region as an original magnetic field using a detection result from the photodetector, the first alternating magnetic field, and the second alternating magnetic field; a second procedure of disposing a measurement target object in the measurement region; a third procedure of causing the first magnetic field generator, the second magnetic field generator, and the third magnetic field generator to generate a magnetic field corresponding to a difference between a target magnetic field which is desired to be formed in the measurement region and the original magnetic field; and a fourth procedure of measuring a magnetic field generated by the measurement target object using the detection result from the photodetector in a period in which the third procedure is being performed and the second procedure is completed.
 10. A magnetic field measurement method of measuring a magnetic field of a measurement region in a magnetic field measurement apparatus in which a first direction, a second direction, and a third direction are perpendicular to each other and which includes a light source that emits light, a medium through which the light passes in the third direction and that changes optical characteristics depending on a magnetic field of the measurement region, a photodetector that detects the optical characteristics, a first magnetic field generator that applies a magnetic field in the first direction to the medium, a second magnetic field generator that applies a magnetic field in the second direction to the medium, and a third magnetic field generator that applies a magnetic field in the third direction to the medium, the method comprising: causing the first magnetic field generator to generate a first alternating magnetic field; causing the second magnetic field generator to generate a second alternating magnetic field which has the same cycle as a cycle of the first alternating magnetic field and has δ as a phase difference relative to the first alternating magnetic field; a first procedure of calculating the magnetic field of the measurement region as an original magnetic field using a detection result from the photodetector, the first alternating magnetic field, and the second alternating magnetic field; a second procedure of disposing a measurement target object in the measurement region; a third procedure of causing the first magnetic field generator to generate a third alternating magnetic field in which a first direction component of a magnetic field corresponding to a difference between a target magnetic field which is desired to be formed in the measurement region and the original magnetic field is added to the first alternating magnetic field, causing the second magnetic field generator to generate a fourth alternating magnetic field in which a second direction component of the magnetic field corresponding to the difference is added to the second alternating magnetic field, and causing the third magnetic field generator to generate a magnetic field having a third direction component of the magnetic field corresponding to the difference; and a fourth procedure of measuring a magnetic field generated by the measurement target object using the detection result from the photodetector, the third alternating magnetic field, and the fourth alternating magnetic field in a period in which the third procedure is being performed and the second procedure is completed.
 11. A magnetic field measurement apparatus in which a first direction, a second direction, and a third direction are perpendicular to each other, the apparatus comprising: a light source that is arranged to emit light; a medium through which the light is arranged to pass in the third direction and that is arranged to change optical characteristics depending on a magnetic field of a measurement region; a photodetector that is arranged to detect the optical characteristics; a first magnetic field generator that is arranged to apply a magnetic field in the first direction to the medium; a second magnetic field generator that is arranged to apply a magnetic field in the second direction to the medium; and a calculation controller that is arranged to cause the first magnetic field generator to generate a first alternating magnetic field, is arranged to cause the second magnetic field generator to generate a second alternating magnetic field which has the same cycle as a cycle of the first alternating magnetic field and has δ as a phase difference relative to the first alternating magnetic field, and is arranged to calculate the magnetic field of the measurement region using a detection result from the photodetector, the first alternating magnetic field, and the second alternating magnetic field. 